论文标题
使用Hessian离散法控制的最佳控制问题的数值分析。
Numerical analysis of optimal control problems governed by fourth-order linear elliptic equations using the Hessian discretisation method
论文作者
论文摘要
本文着重于由Hessian离散方法（HDM）框架中具有夹紧边界条件的四阶线性椭圆方程控制的最佳控制问题。 HDM是一个抽象框架，可以通过称为Hessian离散化（HD）和HD的三个核心属性的四倍体对数值方法进行收敛分析。 HDM涵盖了几种数值方案，例如符合有限元方法，ADINI和MORLEY不合格有限元方法（NCFEMS），基于梯度恢复（GR）运算符和有限体积方法（FVM）的方法。 HDM框架中的状态，伴随和控制变量建立了基本误差估计和超授权结果。本文以数值结果结尾，说明了GR方法ADINI NCFEM和FVM的理论收敛速率。
This paper focusses on the optimal control problems governed by fourth-order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretisation method (HDM). The HDM is an abstract framework that enables the convergence analysis of numerical methods through a quadruplet known as a Hessian discretisation (HD) and three core properties of HD. The HDM covers several numerical schemes such as the conforming finite element methods, the Adini and Morley non-conforming finite element methods (ncFEMs), method based on gradient recovery (GR) operators and the finite volume methods (FVMs). Basic error estimates and superconvergence results are established for the state, adjoint and control variables in the HDM framework. The article concludes with numerical results that illustrates the theoretical convergence rates for the GR method, Adini ncFEM and FVM.
